The electrical images of walls of boreholes in a geological formation, as obtained for example using the tools which are referred to by the references FMI (Full-bore Formation Micro Imager) and/or FMS (Formation Micro Scanner) and have been developed by the company SCHLUMBERGER, are of great benefit to the oil industry because of the wealth of information which they contain. These images are used almost exclusively by structure analysts for fine determination of the geometrical characteristics of the bedding and fracture planes in boreholes.
The FMS and FMI tools make it possible to acquire electrical images from measurements of the local electrical conductivity of the wall of the borehole and, in order to do this, have four articulated arms, each equipped with a pad in the case of the FMS tool, or a pad and a flap (accompanied pad) in the case of the FMI tool. The pads of the FMS tool each have 16 electrodes, and the pads and flaps of the FMI tool each have 24 electrodes. The pads and flaps of the said tools are held against the wall of the borehole using a mechanical system, throughout the acquisition of the electrical images.
An electrical image of the wall of a borehole is a view of the wall of the borehole and, when the borehole is opened to develop the wall on to a plane, has a horizontal axis x representing the azimuthal distribution of the electrodes of the pads and a vertical axis y along which the depth (position) of the tool in the borehole is defined. An FMS or FMI electrical image of the wall in a borehole is reconstructed by 4 or 8 pad images. Since there are 16 electrodes on each pad of the FMS tool and 24 electrodes on each pad and each flap of the FMI tool, a pad (pad or flap) image is therefore formed by 16 or 24 columns (one column per electrode) and several thousand rows, each pixel of the image having a size of about 2.5 mm.sup.2. The vertical sampling interval for the FMS or FMI tool is 2.5 mm, and the lateral sampling shift is 3.8 mm for the FMS tool and 2.5 mm for the FMI tool. More generally, each pad image may be considered, in the aforementioned (x,y) axis system, as consisting of p sample columns (p represents the number of electrodes of the pad), which are each arranged along the y axis and are spaced apart along the x axis by a distance corresponding to the lateral sampling shift, the samples of each column being separated from one another by a distance corresponding to the sampling interval of the tool.
The electrical image is analysed for planar heterogeneities and point heterogeneities. Planar heterogeneity includes the bedding planes as well as the fracture plane of the geological formation which intersect the bedding; the rest of the electrical image represents the point heterogeneities, that is to say the variations which are associated with variations in petrophysical parameters (porosity) or variations in sedimentological parameters (for example bioturbations).
In terms of image analysis, the planar heterogeneities present on the electrical images can be categorized by their conductivity relative to the background of the image, their sharpness (grey scale contrast), their organization (isolated or grouped by family), their frequency (high or low frequency according to direction and depth) and their visibility (visible on all the pad images or only on some of them).
Distinction can be made between four important plane types, which have particular characteristics on the electrical image, namely:
planes which are recognized by the low-frequency variation in the background of the image and which are visible on all the pads, the said planes being identified as the bedding boundaries; PA1 repetitive high-frequency planes, generally with low contrast, always organized by family and visible on all the pads, the said planes representing layering and lying within the beds; PA1 planes which cut the bedding, which have a very high conductivity, are well contrasted and are isolated or organized by family, the said planes being, for the most part, attributable to open fracture planes impregnated with conductive mud; and PA1 planes which also cut the bedding planes, are more or less isolated, conductive or resistive, often less contrasted and generally visible on all the pads, the said planes being interpreted as plugged fracture planes and having a conductivity which depends on the nature of the plugging agent (cement). PA1 segmenting each of the N wall images which are used to reconstruct the image of the side wall of the borehole or of the core sample, into a first set of connected components, each connected component consisting of a homogeneous zone of points which is obtained by grouping points of the traces of the wall image in such a way that the difference in the values taken by a criterion associated with the imaged characteristic, for example a parameter, in particular amplitude, associated with the imaged characteristic, at any two neighbouring points in the said zone has a value below a threshold, PA1 assigning a unique coefficient to all the pixels in a given connected component, the said coefficient being, for example, the mean value of the parameter, in particular amplitude, associated with the imaged characteristic for the trace points grouped in the said connected component, PA1 converting the first set of connected components into a second set consisting only of connected components, referred to as connected regions, which each touch the two edges, right and left, of the image, the said connected regions consisting of all the connected components forming connected regions which are already contained in the first set, and also connected regions which are formed from the connected components of the first set which do not each touch the two edges, right and left, of the image, referred to as connected zones, by merging a given connected zone with the closest neighbouring connected zone, carrying out the merge gradually and, after each merge of two connected zones, reassigning a new coefficient to the resultant connected zone before carrying out a new merge using the remaining connected zones including the said resultant connected zone, PA1 for each pair of consecutive connected regions, generating a smoothed contour marking the boundary of the two connected regions of the said pair by using contour tracking to find an upper envelope contour and a lower envelope contour for the said boundary and by keeping as the smoothed contour that of the two envelope contours which gives a lower variation in the level of the vertical shift; and PA1 producing in the (x,y) axis system an image formed by the connected regions with smoothed contours which are kept, this image being referred to as the bed image associated with the wall image subjected to the segmenting, and the contours between connected regions present on this bed image, referred to as bedding contours, each being representative of a portion of the intersection of a bedding plane with the side wall of the borehole or of the core sample. PA1 a) selecting, from the bedding contours (referred to below as contours) which are present in the N bed images and lie below the sinusoid S.sub.k, a first reference contour chosen from between the contour closest to S.sub.k and the contour encountered first after S.sub.k ; PA1 b) determining, in the bed images which do not contain the first reference contour, the contours of the same polarity which correspond to the said first reference contour and represent N-1 primary contours; PA1 c) constructing all the sinusoids which each contain the first reference contour and incorporate a number of the said primary contours ranging from 1 to N-1, and keeping as the optimum sinusoid S.sub.01 the one of the said sinusoids which has the highest value Q.sub.1, greater than a threshold Q.sub.s, of a predefined criterion Q representative of the quality of the bedding planes; PA1 d) selecting, on the bed image containing the first reference contour, a second reference contour consisting of the contour which has the same polarity as the first reference contour and immediately follows it; PA1 e) determining, in the bed images which do not contain the second reference contour, the contours of the same polarity which correspond to the second reference contour and define N-1 secondary contours; PA1 f) constructing all the sinusoids which each contain the second reference contour and incorporate from 1 to N-1 contours chosen from the set of all the primary and secondary contours, so that there is one contour per image for this choice, and keeping as the optimum sinusoid S.sub.02 the one of the said sinusoids which has the highest value Q.sub.2, greater than the threshold Q.sub.s, of the quality criterion Q; PA1 g) comparing the optimum sinusoids S.sub.01 and S.sub.02 and (i) validating the sinusoid S.sub.01 as the bed boundary S.sub.k+1 if the sinusoid S.sub.02 is parallel to S.sub.01 or if it crosses S.sub.01 and has a value Q.sub.2 of the quality criterion below Q.sub.1, and marking the contours of the validated sinusoid S.sub.01 on the N bed images as the bed boundary S.sub.k+1 or (ii) rejecting the optimum sinusoid S.sub.01 and eliminating the first reference contour if the optimum sinusoid S.sub.02 crosses the sinusoid S.sub.01 and has a value Q.sub.2 of the quality criterion greater than the value Q.sub.1 ; and PA1 h) repeating the series of operations a) to g) using the contours which are present on the N bed images and lie below the sinusoid S.sub.k+1, in the case of operations according to g(i), or below the sinusoid S.sub.k in the case of operations according to g(ii), and as far as the last contours to be matched which are present on the N bed images. PA1 selecting, on each of the N bed images, the first bedding contour (referred to below as contour), PA1 choosing, from the said selected first contours, the contour having least depth as the reference contour, PA1 determining, in the bed images which do not contain the reference contour, the contours of the same polarity which correspond to the reference contour and define N-1 primary contours; and PA1 constructing the optimum sinusoid S.sub.1 either (i) by picking or (ii) by applying the process according to points c) to g) described above. PA1 a, b, c, d and e represent weightings for the criteria to which they relate, it being advantageous for the said weightings to take the value 1, in the case of a, b, c and d, and the value 2 in the case of e; PA1 Qgd represents the local contrast of the plane on the image of the gradient, the said local contrast giving account of the contrast between beds and being expressed by the equation Qgd=Mgd: Vgd, where Mgd is the mean of the gradients along the sinusoid estimated over the N wall images which are filtered by the filter appertaining to the one-dimensional gradient Gy along the y direction, and Vgd is the standard deviation of the images of the gradient, as it is calculated over all the N wall images; PA1 Qct represents the overall contrast of the plane, the said overall contrast giving account of the low-frequency contrasts along the sinusoid and being expressed as the mean of the N/2 differences .DELTA. with lowest absolute values taken from the series of the N differences .DELTA., each of which corresponds to one of the N images and represents the difference between the mean values of amplitude in the upper bed and the lower bed as they are calculated in two windows along the sinusoid just above and below the plane in the image in question; PA1 Qcr represents the overall correlation between the N images, the said correlation giving account of the homogeneity of the texture enclosing the sinusoid and being defined by the equation: ##EQU2## where Vup and Vlo are respectively the standard deviations of the amplitudes which are associated, on the one hand, with the upper bed and, on the other hand, with the lower bed, the standard deviations being calculated in the same window as for Qct, over the N images and V.sub..DELTA. is the standard deviation of the N differences .DELTA. as they are defined above; PA1 Qdy represents the planarity or roughness of the plane, which is expressed by the equation Qdy=1/.DELTA.Ey' PA1 Qm represents the number of images retained for matching the sinusoid.
When a plane, which may be one or other of the aforementioned planes, intersects a cylindrical borehole wall whose axis is not perpendicular to the plane, the intersection is seen on the image of the borehole wall as a sinusoid with equation y=d+A sin (x+.phi.), in which the amplitude A and the phase .phi. correspond respectively to the dip and the azimuth of the plane, d being the depth at which the sinusoid is located.
The concept of a "bed" is one of the fundamental concepts used by geologists on site or by sedimentologists, who work on core samples of the geological formation, for studying the facies of sedimentary units. The beds are defined as being low-frequency planar heterogeneities. They are generally more highly contrasted and much thicker than the layering, and their thickness can vary greatly, for example, a few centimetres to a few meters. The bed boundaries can be marked by grey-scale contrasts exhibiting an abrupt transition or a smooth transition; they may also be characterized simply by a change in texture.
Manual picking of the bedding planes on the borehole wall images is a basic skill, but one which proves very complex and tedious.
Automatic plane recognition from electrical borehole wall images also entails significant difficulties, on the one hand due to the low image coverage factor (an image divided into 4 or 8 pad images corresponding to a coverage factor of 40% to 80%), and on the other hand due to the interference which occurs between the geological heterogeneities. If the coverage factor of the image were 100%, the problem of recognizing the sinusoids describing the intersections of the planes with the wall of the borehole could be likened to a simple problem of extracting lines from the images. However, for a low image coverage factor as mentioned above, this problem becomes a problem, which is much more complex to solve, of recognizing sinusoids defined by portions, and furthermore with additional constraints connected with the vertical spacing between the pad images.
Two methods have been described for automatically determining dips and azimuths of the planes intersecting a borehole drilled in a geological formation, on the basis of wall images of the said borehole, one using matching between the current lines (contours) in the case of electrical images (J. N. ANTOINE and J. P. DELHOMME: "A method to derive dips from bed boundaries in borehole images", Paper SPE 20 540 .OMEGA. (1990), pages 121 to 130, and also U.S. Pat. No. 5,299,128), and the other resorting to the HOUGH transform (U.S. Pat. No. 3,069,654) to process acoustic images (D. TORRES, R. STRICKLAND and M. GIANZERO: "A new approach to determining dip and strike using borehole images", SPWLA, 31.sup.st Annual Logging Symposium, Jun. 24-27, 1990).
However, no method has yet been proposed which satisfactorily solves the problem of determining the bedding in a formation, in particular a geological formation, from images of the wall of a borehole made in the said formation or, which is equivalent, from images of the side surface of core samples of this formation.